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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 5
  3. Calculus of Variations and Partial Differential Equations : Volume 5, Issue 2, June 1997
  4. On the thread problem for minimal surfaces
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5
Calculus of Variations and Partial Differential Equations : Volume 5, Issue 6, September 1997
Calculus of Variations and Partial Differential Equations : Volume 5, Issue 5, July 1997
Calculus of Variations and Partial Differential Equations : Volume 5, Issue 2, June 1997
Minimal surfaces in a wedge I. Asymptotic expansions
On the thread problem for minimal surfaces
Convergence of eigenvalues and Green functions under surgery type degeneration of Riemannian manifolds
A multibump construction in a degenerate setting
Harmonic maps with potential
Calculus of Variations and Partial Differential Equations : Volume 5, Issue 4, May 1997
Calculus of Variations and Partial Differential Equations : Volume 5, Issue 3, March 1997

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On the thread problem for minimal surfaces

Content Provider SpringerLink
Author Pilz, Robert
Copyright Year 1997
Abstract For a given one-dimensional fixed boundary Γ in ℝ3 and a given constant c<0 we consider any one-dimensional free boundary F in ℝ3 subject to the conditions that the length of F is equal to c, that Γ and F form a closed boundary, and that the minimal surface S of dimension two being bounded by Γ and F minimizes the area among all comparison surfaces $$\tilde S$$ being bounded by Γ and some $$\tilde F$$ with length equal to c.This variational problem is known as the thread problem for minimal surfaces and stems from soap film experiments, in which the fixed boundary parts are pieces of wires and the free boundary parts are threads.The new result of this article will be that F has no singular points in ℝ3∖Γ, provided the admissible surfaces and boundary parts are supposed to be rectifiable flat chains modulo two.
Ending Page 136
Page Count 20
Starting Page 117
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 2
Volume Number 5
Language English
Publisher Springer-Verlag
Publisher Date 1997-01-01
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Variational problems in a geometric measure-theoretic setting Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Mathematical and Computational Physics Optimization of shapes other than minimal surfaces Minimal surfaces, surfaces with prescribed mean curvature
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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